Research Article
Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation
Table 3
Frequency equations and corresponding constants in mode shapes for ten degenerate cases with
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| | Case | Frequency equation | c1 | c2 | c3 | c4 |
| | Sl-Fi | | 1 | c2,S1Fi | 1 | c4,S1Fi | | Fr-Sl | | 1 | | 1 | | | Fr-Fi | | 1 | | 1 | | | Pi-Sl | | 1 | 0 | | 0 | | Sl-Sl | | 1 | c2,S1S1 | 1 | c4,S1S1 | | Pi-Pi | | 1 | 0 | 0 | 0 | | Fr-Fr | | 1 | | 1 | | | Fi-Fi | | 1 | | 1 | | | Fr-Pi | | 1 | | 1 | | | Pi-Fi | | 1 | 0 | | 0 |
| | Sl-Fi | | c1,S1Fi | 1 | 1 | | | Fr-Sl | | 0 | 1 | 1 | c4,FrS1 | | Fr-Fi | | 0 | 1 | 1 | c4,FrFr | | Pi-Sl | | 0 | 1 | c3,PiS1 | 0 | | Sl-Sl | | c1,S1S1 | 1 | 1 | c4,S1S1 | | Others | — | — | — | — | — |
| | Sl-Fi | | 1 | −5 | 0 | | | Fr-Sl | | 1 | −2.5 | 0 | 0 | | Fr-Fi | | 1 | −5 | 0 | 0 | | Pi-Sl | | 1 | 0 | −10 | 0 | | Sl-Sl | | 1 | −2.5 | 0 | | | Others | — | — | — | — | — |
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, , , and . , , , , , and . : “ ” = none. |
